B: Don't need ExtractBetween, use ExtractAfter; then don't need the actual \n in the data
C: Don't worry about stopping; just delete after the last line of interest although is very long the fgetl route is still a possibility not to discount.
hdr=readlines(websave('TEST_readingTextFile_MATLAB.txt','https://www.mathworks.com/matlabcentral/answers/uploaded_files/1151100/TEST_readingTextFile_MATLAB.txt'));
hdr=hdr(strlength(hdr)>0);
idxData=find(matches(hdr,"AMPLITUDE EQUALIZED"))+3;
data=hdr(idxData:end);
hdr=hdr(1:idxData-1);
ixTime=find(contains(hdr,'recording:'));
tStart= datetime(strtrim(extractAfter(hdr(ixTime(1)),'ing:')),'inputformat',"dd/MM/uuuu HH:mm:ss")
tEnd= datetime(strtrim(extractAfter(hdr(ixTime(2)),'ing:')),'inputformat',"dd/MM/uuuu HH:mm:ss")
Q2: Again, read the whole thing and then just keep what don't want/need instead of worrying about skipping on reading -- will be just as fast (or maybe even faster as file sizes grows). I'd also recommend to look at timetable as another possible data storage mechanism depending upon what is to be done with data in end.
data=str2double(split(data))
If the above turns out to be slow with full-length files, post back and we'll attack speeding up -- it would basically be a mesh of what you've done and the above...
